1. Field of the Invention
Embodiments of the present invention relate generally to a method of measuring the thickness of a thin layer in a semiconductor device, and an apparatus for performing the method. More particularly, embodiments of the invention relate to a method and apparatus for measuring the thickness of a thin layer using a regression fitting process.
A claim of priority is made to Korean Patent Application No. 2005-65878, filed on Jul. 20, 2005, the disclosure of which is hereby incorporated by reference in its entirety.
2. Description of Related Art
Modern semiconductor devices tend to include several thin layers formed on a substrate. These thin layers are generally formed by performing several thin layer forming processes in sequence on the substrate. A typical semiconductor device includes, for example, an insulation layer, a dielectric layer, and a metal layer formed sequentially on a substrate such as a silicon wafer. In addition to the thin layer forming processes, patterning processes such as etching and photolithography are also performed to create patterns in the thin layers.
The physical characteristics of each thin layer, such as thickness, chemical composition, and optical coefficients (e.g., refractive index and extinction coefficient), can affect the way a semiconductor device performs. Moreover, the physical characteristics of each layer can affect the way that layers are subsequently formed and therefore how the subsequently formed layers behave. As a result, semiconductor manufacturers like to monitor the physical characteristics of thin layers as they are formed to ensure the quality of the semiconductor devices.
Monitoring the physical characteristics of each layer in a semiconductor device becomes more important as the integration density of the device increases because as the features of a semiconductor device become smaller, it becomes more likely that small variations in the physical characteristics of each thin layer will affect the device's performance. One example of how small variations in the physical characteristics of a thin layer can affect a device's performance is provided by a gate oxide layer used to form a transistor. Where the gate oxide layer is too thin, it may break down under normal operating conditions, corrupting the device.
One way to measure the physical characteristics of a thin layer involves forming the thin layer on a wafer and then cutting the wafer into a plurality of specimens that can be analyzed using an electron-based imaging apparatus such as a vertical scanning electron microscope (VSEM). Unfortunately, this method is both costly and time consuming, and as a result, researchers have developed other “non-destructive” techniques, i.e., techniques that do not require cutting up a wafer, for measuring the physical characteristics of a thin layer.
Several of the non-destructive techniques rely on optical technology to measure the physical properties of thin layers. However, because layers formed beneath the thin layer can create optical distortion, e.g., in the form of interference, the optical techniques are generally not applied to a working wafer where a semiconductor device is formed. Instead, these techniques are commonly applied to a monitoring wafer on which a thin layer is formed using the same thin layer processes performed on the working wafer. Then, the measurements obtained from the monitoring wafer are used to infer the properties of the thin layer formed on the working wafer.
Unfortunately, conventional optical technologies for measuring the physical characteristics of a thin layer still suffer from a variety of inaccuracies and inefficiencies. For example, characteristics inferred from measurements performed on the monitoring wafer may not accurately reflect the true characteristics of the thin layer on the working wafer. In addition, processes for forming a thin layer on the monitoring wafer increase the time and cost of manufacturing a semiconductor device.
To address the drawbacks of these conventional approaches, a dual beam spectrometry process and a spectroscopic ellipsometry process have been developed to measure the thickness of a thin layer formed in a multilayer structure including a plurality of thin layers.
Both the dual beam spectrometry process and the spectroscopic ellipsometry process can use a combination of measured values and theoretical values to generate estimates for the physical properties of a thin layer. For instance, the thickness of the thin layer can be computed by obtaining measurements related to the thickness and then finding a theoretical function that is a “best fit” to the measurements. The theoretical function is generated from a putative thickness of a hypothetical layer. The putative thickness (also called “presumptive” thickness or “assumed” thickness) is a temporary thickness estimate used in the estimation process. Eventually, the putative thickness is stored as an “actual” thickness. The putative thickness that corresponds to the “best fit” function is then generated as the estimate of the thin layer's thickness. An example of a spectroscopic ellipsometry process that uses theoretical and measured values to generate an estimate of the thickness of a thin layer in a semiconductor device is described briefly below.
In the spectroscopic ellipsometry process, polarized light is reflected off of the thin layer and then various properties of the reflected light are measured and used to estimate the thickness of the layer. In particular, a spectroscopic ellipsometer measures an amplitude change and a phase shift of the reflected light as a function of the light's various wavelengths. These measurements, also called measured signals, are collected for a range of wavelengths contained in the polarized light to generate a “measured signal spectrum” for the thin layer. The amplitude change and phase shift are used to determine a reflectance ratio defined as an intensity of a first reflected component that oscillates parallel to a plane of incidence divided by the intensity of a second reflected component that oscillates parallel to a plane of a sample surface of the thin layer. Due to their respective orientations relative to the surface of the thin layer, the first reflected component will be referred to as a vertical component and the second reflected component will be referred to as a horizontal component.
In general, a thin layer with a known thickness has a corresponding “theoretical signal spectrum” which one would expect to match with the layer's measured signal spectrum. For a given measurement process, there is typically a mapping between the thickness and the theoretical signal spectrum such that if either the thickness or the theoretical signal spectrum is known, the other can be inferred or derived. Because measurements are rarely one hundred percent precise, the theoretical signal spectrum of a thin layer with a known thickness may vary from the thin layer's measured signal spectrum. Accordingly, where the measured signal spectrum of a thin layer is known, a corresponding theoretical signal spectrum can be identified as the theoretical signal spectrum that best approximates the measured signal spectrum. A thickness of the thin layer can then be derived from the identified theoretical signal spectrum.
FIGS. 1A and 1B show concrete examples of theoretical and measured signal spectra obtained by reflecting polarized light off of a thin layer using a spectroscopic ellipsometer manufactured by Nanometrics. The polarized light is reflected off of the thin layer at an angle of 65°. In FIGS. 1A and 1B, the theoretical signal spectra are denoted by solid curves and the measured signal spectra are denoted by dotted curves.
In FIG. 1A, various wavelengths of the reflected light are plotted against an inverse tangent of the reflectance ratio of the vertical and horizontal components. In FIG. 1B, various wavelengths of the reflected light are plotted against a phase change of the reflected light. The inverse tangent of the reflectance ratio and the phase change were calculated based on ellipsometry theory.
A conventional approach to measuring the similarity between the measured signal spectrum and the theoretical spectrum is a “goodness of fit” (GOF) criteria based on a mean square error (MSE) function in statistics. The MSE is based on a difference between the measured signal spectrum and the theoretical signal spectrum. The difference between the measured signal spectrum and the theoretical signal spectrum is referred to in this description as a “skew signal spectrum” and the difference between a measured signal and a corresponding theoretical signal defined with respect to the same wavelength is referred to as a “skew signal.”
For a measured signal spectrum/theoretical signal spectrum pair, the GOF criteria defines a GOF value between zero (0) and one (1). Where the measured signal spectrum and the theoretical signal spectrum are the same, the GOF value is one (1). As the dissimilarity between the measured and theoretical signal spectra increases, the GOF value tends toward zero. Unfortunately, the GOF value may not accurately reflect the level of similarity between the measured signal spectrum and the theoretical spectrum.
For example, in FIGS. 1A and 1B, the measured signal spectrum and the theoretical signal spectrum are visibly dissimilar from each other, but the GOF value is about 0.976, which is relatively high. Conventional optimization techniques could be used to further increase the GOF value to about 0.99.
The way to maximize the GOF value between a theoretical signal spectrum and the measured signal spectrum is to find a theoretical signal spectrum as close to the measured signal spectrum as possible. One way to do this is by a “regression fitting process.” In the regression fitting process, a putative thickness for the thin layer is chosen and then the theoretical signal spectrum is computed based on the putative thickness. Then, the GOF value is computed for the theoretical signal spectrum and the measured signal spectrum. If the GOF value is above a predetermined threshold, the putative thickness is assumed to be the actual thickness of the thin layer. However, if the GOF value is below the predetermined threshold, the putative thickness is updated and the process of computing the theoretical spectrum is repeated.
Because the GOF value is based on the difference between the theoretical signal spectrum and the measured signal spectrum, the GOF value tends to be relatively high if the measured signal spectrum has a simple shape or is distributed over a small range. This is true even if the actual shapes of the theoretical and measured signal spectra differ significantly since the actual difference between two curves both distributed over a small range is generally small. However, where the measured and theoretical signal spectra are distributed over a large range and have a complicated shape, the GOF value may be small even if the theoretical and measured signal spectra appear to be very similar. FIG. 2 and FIGS. 3A and 3B demonstrate a relationship between the GOF value and the range of the theoretical and measured signal spectra.
FIG. 2 is a view illustrating the measured and theoretical signal spectra of a light reflected from a thin layer formed to a thickness of about 15,000 Å on a wafer. The experimental conditions for the results shown in FIG. 2 are the same as the conditions for the experimental results shown in FIGS. 1A and 1B. FIG. 2 shows a graph of the inverse tangent of a reflectance ratio of the vertical and horizontal components of the reflected light as a function of the wavelength of the light. In FIG. 2, the measured and theoretical signal spectra are almost identical to each other and their GOF value is about 0.976. No matter how many times the conventional regression fitting process is repeated on the data shown in FIG. 2, their GOF value will not exceed 0.976. Accordingly, FIGS. 1A and 1B and FIG. 2 demonstrate that the same GOF value may indicate very different levels of similarity depending on the range and shape of the measured signal spectrum.
The measured signal spectrum in FIG. 1B ranges between about 20 and 27, while the measured signal spectrum in FIG. 2 ranges from about 20 to 80. While the measured signal spectrum in FIG. 1B has a relatively simple shape, the measured signal spectrum in FIG. 2 has a relatively complicated shape.
FIG. 3A shows a skew signal spectrum for the theoretical and measured signal spectra in FIG. 1A, and FIG. 3B shows a skew signal spectrum for the theoretical and measured signal spectra in FIG. 2. Even though the measured and theoretical signal spectra in FIG. 2 appear to be more similar than the measured and theoretical signal spectra in FIG. 1A, the ranges of their respective skew signal spectra are very similar.
The skew signal spectrum shown in FIG. 3A is the result of a poor regression fitting process, and the skew signal spectrum shown in FIG. 3B is the result of a good regression fitting process. However, in both cases, the range of the skew signal spectrum is small, and therefore the GOF value is close to one (1). In particular, the skew signal spectrum shown in FIG. 3A has a maximum value of about +1.534 and a minimum value of about −1.226 and the skew signal spectrum shown in FIG. 3B has a maximum value of about +1.285 and a minimum value of about −1.319. Since the GOF criteria does not distinguish a poor regression fitting process from a good regression fitting process, an improved measure of the similarity between the measured and theoretical signal spectra is desired.